%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO190+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n016.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Sat Jul 16 07:00:35 EDT 2022 % Result : Theorem 0.35s 0.53s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO190+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n016.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sat Jun 18 03:50:06 EDT 2022 % 0.13/0.34 % CPUTime : % 0.35/0.53 (* PROOF-FOUND *) % 0.35/0.53 % SZS status Theorem % 0.35/0.53 (* BEGIN-PROOF *) % 0.35/0.53 % SZS output start Proof % 0.35/0.53 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\((distinct_points X Z)/\((distinct_points Y Z)/\(~(apart_point_and_line Z (line_connecting X Y))))))->(~(apart_point_and_line Z (line_connecting Y X))))))). % 0.35/0.53 Proof. % 0.35/0.53 assert (zenon_L1_ : forall (zenon_TY_s : zenon_U) (zenon_TX_t : zenon_U), (forall Z : zenon_U, ((distinct_points zenon_TX_t zenon_TY_s)->((distinct_points zenon_TX_t Z)\/(distinct_points zenon_TY_s Z)))) -> (distinct_points zenon_TX_t zenon_TY_s) -> (~(distinct_points zenon_TY_s zenon_TX_t)) -> False). % 0.35/0.53 do 2 intro. intros zenon_Hf zenon_H10 zenon_H11. % 0.35/0.53 generalize (zenon_Hf zenon_TX_t). zenon_intro zenon_H14. % 0.35/0.53 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ]. % 0.35/0.53 exact (zenon_H16 zenon_H10). % 0.35/0.53 apply (zenon_or_s _ _ zenon_H15); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 0.35/0.53 generalize (apart1 zenon_TX_t). zenon_intro zenon_H19. % 0.35/0.53 exact (zenon_H19 zenon_H18). % 0.35/0.53 exact (zenon_H11 zenon_H17). % 0.35/0.53 (* end of lemma zenon_L1_ *) % 0.35/0.53 assert (zenon_L2_ : forall (zenon_TY_s : zenon_U) (zenon_TX_t : zenon_U), (apart_point_and_line zenon_TX_t (line_connecting zenon_TX_t zenon_TY_s)) -> (distinct_points zenon_TX_t zenon_TY_s) -> False). % 0.35/0.53 do 2 intro. intros zenon_H1a zenon_H10. % 0.35/0.53 generalize (ci1 zenon_TX_t). zenon_intro zenon_H1b. % 0.35/0.53 generalize (zenon_H1b zenon_TY_s). zenon_intro zenon_H1c. % 0.35/0.53 apply (zenon_imply_s _ _ zenon_H1c); [ zenon_intro zenon_H16 | zenon_intro zenon_H1d ]. % 0.35/0.53 exact (zenon_H16 zenon_H10). % 0.35/0.53 exact (zenon_H1d zenon_H1a). % 0.35/0.53 (* end of lemma zenon_L2_ *) % 0.35/0.53 assert (zenon_L3_ : forall (zenon_TX_t : zenon_U) (zenon_TY_s : zenon_U), (apart_point_and_line zenon_TY_s (line_connecting zenon_TX_t zenon_TY_s)) -> (distinct_points zenon_TX_t zenon_TY_s) -> False). % 0.35/0.53 do 2 intro. intros zenon_H1e zenon_H10. % 0.35/0.53 generalize (ci2 zenon_TX_t). zenon_intro zenon_H1f. % 0.35/0.53 generalize (zenon_H1f zenon_TY_s). zenon_intro zenon_H20. % 0.35/0.53 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H16 | zenon_intro zenon_H21 ]. % 0.35/0.53 exact (zenon_H16 zenon_H10). % 0.35/0.53 exact (zenon_H21 zenon_H1e). % 0.35/0.53 (* end of lemma zenon_L3_ *) % 0.35/0.53 apply NNPP. intro zenon_G. % 0.35/0.53 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\((distinct_points X Z)/\((distinct_points Y Z)/\(~(apart_point_and_line Z (line_connecting X Y))))))->(~(apart_point_and_line Z (line_connecting Y X))))))) zenon_G); [ zenon_intro zenon_H22; idtac ]. % 0.35/0.53 elim zenon_H22. zenon_intro zenon_TX_t. zenon_intro zenon_H23. % 0.35/0.53 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((distinct_points zenon_TX_t Y)/\((distinct_points zenon_TX_t Z)/\((distinct_points Y Z)/\(~(apart_point_and_line Z (line_connecting zenon_TX_t Y))))))->(~(apart_point_and_line Z (line_connecting Y zenon_TX_t)))))) zenon_H23); [ zenon_intro zenon_H24; idtac ]. % 0.35/0.53 elim zenon_H24. zenon_intro zenon_TY_s. zenon_intro zenon_H25. % 0.35/0.53 apply (zenon_notallex_s (fun Z : zenon_U => (((distinct_points zenon_TX_t zenon_TY_s)/\((distinct_points zenon_TX_t Z)/\((distinct_points zenon_TY_s Z)/\(~(apart_point_and_line Z (line_connecting zenon_TX_t zenon_TY_s))))))->(~(apart_point_and_line Z (line_connecting zenon_TY_s zenon_TX_t))))) zenon_H25); [ zenon_intro zenon_H26; idtac ]. % 0.35/0.53 elim zenon_H26. zenon_intro zenon_TZ_bn. zenon_intro zenon_H28. % 0.35/0.53 apply (zenon_notimply_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 0.35/0.53 apply zenon_H29. zenon_intro zenon_H2b. % 0.35/0.53 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H10. zenon_intro zenon_H2c. % 0.35/0.53 apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H2e. zenon_intro zenon_H2d. % 0.35/0.53 apply (zenon_and_s _ _ zenon_H2d). zenon_intro zenon_H30. zenon_intro zenon_H2f. % 0.35/0.53 generalize (cu1 zenon_TX_t). zenon_intro zenon_H31. % 0.35/0.53 generalize (apart4 zenon_TX_t). zenon_intro zenon_H32. % 0.35/0.53 generalize (zenon_H31 zenon_TY_s). zenon_intro zenon_H33. % 0.35/0.53 generalize (ci1 zenon_TY_s). zenon_intro zenon_H34. % 0.35/0.53 generalize (zenon_H32 zenon_TY_s). zenon_intro zenon_Hf. % 0.35/0.53 generalize (ceq2 zenon_TZ_bn). zenon_intro zenon_H35. % 0.35/0.53 generalize (ci2 zenon_TY_s). zenon_intro zenon_H36. % 0.35/0.53 generalize (zenon_H34 zenon_TX_t). zenon_intro zenon_H37. % 0.35/0.53 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H11 | zenon_intro zenon_H38 ]. % 0.35/0.53 apply (zenon_L1_ zenon_TY_s zenon_TX_t); trivial. % 0.35/0.53 generalize (zenon_H36 zenon_TX_t). zenon_intro zenon_H39. % 0.35/0.53 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H11 | zenon_intro zenon_H3a ]. % 0.35/0.53 apply (zenon_L1_ zenon_TY_s zenon_TX_t); trivial. % 0.35/0.53 generalize (zenon_H35 (line_connecting zenon_TY_s zenon_TX_t)). zenon_intro zenon_H3b. % 0.35/0.53 generalize (zenon_H3b (line_connecting zenon_TX_t zenon_TY_s)). zenon_intro zenon_H3c. % 0.35/0.53 apply (zenon_imply_s _ _ zenon_H3c); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ]. % 0.35/0.53 exact (zenon_H3e zenon_H2b). % 0.35/0.53 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 0.35/0.53 generalize (zenon_H33 (line_connecting zenon_TY_s zenon_TX_t)). zenon_intro zenon_H41. % 0.35/0.53 generalize (zenon_H41 (line_connecting zenon_TX_t zenon_TY_s)). zenon_intro zenon_H42. % 0.35/0.53 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 0.35/0.53 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H16 | zenon_intro zenon_H45 ]. % 0.35/0.53 exact (zenon_H16 zenon_H10). % 0.35/0.53 exact (zenon_H45 zenon_H40). % 0.35/0.53 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.35/0.53 exact (zenon_H3a zenon_H47). % 0.35/0.53 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H1a | zenon_intro zenon_H48 ]. % 0.35/0.53 apply (zenon_L2_ zenon_TY_s zenon_TX_t); trivial. % 0.35/0.53 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H49 | zenon_intro zenon_H1e ]. % 0.35/0.53 exact (zenon_H38 zenon_H49). % 0.35/0.53 apply (zenon_L3_ zenon_TX_t zenon_TY_s); trivial. % 0.35/0.53 exact (zenon_H2f zenon_H3f). % 0.35/0.53 Qed. % 0.35/0.53 % SZS output end Proof % 0.35/0.53 (* END-PROOF *) % 0.35/0.53 nodes searched: 576 % 0.35/0.53 max branch formulas: 345 % 0.35/0.53 proof nodes created: 79 % 0.35/0.53 formulas created: 2804 % 0.35/0.53 %------------------------------------------------------------------------------